The factorial function is defined for positive integers as n! = n(n - 1)(n - 2) · · · 3 • 2 • 1. For example, 5! = 5 • 4 • 3 • 2 • 1 = 120. A valuable result that gives good approximations to n! for large values of n is Stirling’s formula, n! ≈ √2πn nⁿe^-n. Use this formula and a calculator to determine where the factorial function appears in the ranking of growth rates given in Theorem 4.15.